Geometry Based Prediction of Laminar Flow Characteristics through Non-Homogeneous Porous Media
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameMaster of Engineering
The prediction of flow rate and local pressure for Darcian flow through porous media that is non-homogenous in the direction of bulk fluid flow has previously been achieved through the use of numerical simulations. This thesis develops a model to predict Darcian flow behaviour by building a non-dimensional representation of flow through Cartesian geometries that are non-homogeneous along the direction of bulk flow. To construct the model, simulations were conducted in COMSOL™ by numerically modelling laminar flow through a tortuous Cartesian geometry and then normalising the results to produce a non-dimensional representation of flow behaviour as a function of the geometry. Through this method the permeability of the simulation domain was related to geometrical parameters. By splitting the geometry into simply defined ‘blocks’ the relationship between the permeability of the block to fluid flow was clearly defined with regard to the characteristic block length. The simulations were conducted across two case studies. The first case study examined the flow characteristics through a geometry with the characteristic length varying along the direction of bulk fluid flow. The major outcome of this case study was to prove that the block permeability was proportional to the square of the characteristic length of the block. In addition it is shown that the when the geometry varies, the flow rate and local pressure through a tortuous series of connected non-homogeneous blocks could be predicted using a linear equation within a maximum error of -0.4% and ~2 Pa (when the total pressure drop was 1000 Pa) respectively. The second case study expanded the length variation to include the variation of the characteristic lengths perpendicular to the direction of bulk fluid flow. The resulting data was used to create a model that successfully predicts the permeability, flow rate and local pressure through tortuous geometries that are non-homogeneous parallel and perpendicular to the path of bulk fluid flow. Local pressure was predicted with a maximum error of 2.5 Pa. The model developed in this thesis provides the foundation for developing a method that could decouple Fluid-Solid interface simulations in the field of deformable porous media, other future directions for this research are also discussed. Currently, the method can provide a tool to predict Darcian flow through non-homogeneous porous media.